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A Spanning Series Approach to Options

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  • Steven L. Heston
  • Alberto G. Rossi

Abstract

This paper shows that Edgeworth expansions for option valuation are equivalent to approximating option payoffs using Hermite polynomials. Consequently, the value of an option is the value of an infinite series of replicating polynomials. The resultant formulas express option values in terms of skewness, kurtosis, and higher moments. Unfortunately, the Hermite series diverges for fat-tailed models, so we provide alternative moment-based formulas. These formulas are a computationally efficient alternative to Fourier transform valuation and can value options even when the characteristic function is unknown. Applications include the first convergent solution for Hull and White’s stochastic volatility model.Received February 1, 2016; accepted June 27, 2016 by Editor Wayne Ferson.

Suggested Citation

  • Steven L. Heston & Alberto G. Rossi, 2017. "A Spanning Series Approach to Options," The Review of Asset Pricing Studies, Oxford University Press, vol. 7(1), pages 2-42.
  • Handle: RePEc:oup:rapstu:v:7:y:2017:i:1:p:2-42.
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    References listed on IDEAS

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    Cited by:

    1. Falko Baustian & Katev{r}ina Filipov'a & Jan Posp'iv{s}il, 2019. "Solution of option pricing equations using orthogonal polynomial expansion," Papers 1912.06533, arXiv.org, revised Jun 2020.

    More about this item

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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